z-test

ztest.R

# we seek to test whether two parameters, say theta1 and theta2, are diff from each other, using a z-test
# we assume we have an estimate of the thetaj's (mle1 and mle2) and associated standard errors (se1 and se2)
# we write a function that calculate the z-statistic and return the p-value (both-sided test)

# function
ztest <- function(mle1, mle2, se1, se2){
  stat <- (mle1 - mle2)/sqrt(se1^2+se2^2)
  pvalue <- ifelse(stat > 0, 2 * pnorm(stat, lower.tail = FALSE), 2 * pnorm(stat, lower.tail = TRUE))
  return(data.frame("z-score" = stat, "p-value" = pvalue))
}

# example
m1 <- 0.8
m2 <- 0.6
ste1 <- 0.06
ste2 <- 0.05

ztest(m1, m2, ste1, ste2)